Impact sockets are made with a softer steel that can handle impacts better. They are thicker because the steel is in fact softer and easier to bend (but not necessarily break). The reason softer steel can take impacts better is that as you impact it, the entire piece of metal compresses a tiny bit, dispersing the energy of the impact throughout the entire socket.
Chrome sockets are made from a harder steel that is also stronger, but it is more brittle and cannot take impacts well. When you impact harder steel, the energy from the impact doesn't disperse as well, and you end up with all the force of the impact being absorbed by a very small portion of the socket (very likely just the surface of it). This creates more stress even though the total force is the same, and causes a crack to form. Once the crack starts, it propagates and the socket can shatter.
Remember, stress is equal to force divided by cross-sectional area. It describes how much force a certain amount of a material is subjected to. Softer metals allow the force to be shared by the entire piece of metal more easily. More brittle metals can withstand more force if you load them up slowly, but when you impact them they can shatter.
It's also worth mentioning that impact sockets wear out faster than chrome sockets, especially if you use them with a normal ratchet. Because the metal is softer, it wears away and deforms a very tiny bit when you use it, and this adds up over the years. Chrome sockets are still worth keeping around--they will last you a lot longer if you use them properly.
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